autobeaming exception help needed

[Kieren MacMillan]

Hello, all —

I clearly don't quite understand the new autobeaming and exception system 
(2.15.14), and R-ing the FM has not helped…  =(

My piece switches back and forth between 4/4, 3/4, and 2/4. Regardless of the 
time signature, what I want is:
    a) Quarter-note groupings for 8th notes (i.e., two eighth notes with a 
single unbroken beam), triplet 8th notes (i.e., three eighth notes with a 
single unbroken beam), and 16th notes (i.e., four 16th notes with two unbroken 
beams); and,
    b) Eighth-note groupings for sextuplet 16th notes (i.e., one unbroken beam 
connecting two groups of three 16th notes each with two unbroken beams) and 
32nd notes (i.e., one unbroken beam connecting two groups of four 32nd notes 
each with three unbroken beams).

I've tried a couple of different things, but it seems like I can't get the 
right combination of rules. In particular, every time the time signature 
changes, it seems like I have to reset the exceptions.

The closest I've gotten to what I want is:

\version "2.15.14"
beamtest = \relative c'' {
  \set subdivideBeams = ##t
  \set baseMoment = #(ly:make-moment 1 8)
  \time 3/4 c16 c c c \times 2/3 { c16 c c c c c } c32 c c c c c c c   |
  \time 4/4 c16 c c c \times 2/3 { c16 c c } \times 2/3 { c c c } \times 2/3 { 
c8 c c } c32 c c c c c c c   |
  \time 3/4 c16 c c c \times 2/3 { c16 c c c c c } c32 c c c c c c c   |
  \time 4/4 c16 c c c \times 2/3 { c16 c c } \times 2/3 { c c c } \times 2/3 { 
c8 c c } c32 c c c c c c c   |
}
\score { \beamtest }

Now I just need to make the sixteenth notes NOT break at the eighth.

Any help would be appreciated.

Thanks!
Kieren.